I have a question:
Would Gravity (or gravitational) waves be considered mechanical waves?
Wouldn't the Medium be the space-time continuum itself for these waves?

Well, to my knowledge, not many mechanical waves are qudripole like a gravitational wave is. You are correct in assuming that space-time is the medium for such waves, however. As in it's the local value of the metric (the value of curvature) that changes as said gravitational wave passes through.